The main purpose of this assignment is for you to gain experience using tree-based methods

to solve simple regression problems. In this assignment, you will fit a Gradient-Boosted

Regression Tree, a Random Forest, and a Decision Tree to a noisy 3D sinusoidal

data set. Since these models can be trained very quickly on the supplied data, I want you to

first manually adjust hyperparameter values and observe their influence on the model's

predictions. That is, you should manually sweep the hyperparameter space and try to hone

in on the optimal hyperparameter values, again, manually. (Yep, that means guess-and-

check: pick some values, train the model, observe the prediction curve, repeat.)

But wait, there's more! Merely attempting to identify the optimal hyperparameter values is

not enough. Be sure to really get a visceral understanding of how altering a hyperparameter

in turn alters the model predictions (i.e. the prediction curve). This is how you will build your

machine learning intuition!

So, play around and build some models. When you are done playing with hyperparameter

values, you should try to set these values to the optimal values manually (you're likely going

to be way off). Then, retrain the model. Next in this assignment, we will perform several grid

searches, so you'll be able to compare your "optimal" hyperparameter values with those

computed from the grid search.

We will visualize model predictions for the optimal Gradient-Boosted Regression

Tree, a Random Forest, and Decision Tree models that were determined by the grid

searches. Next, you will compute the generalization error on the test set for the three

models.